v.vol.rst  Interpolates point data to a 3D raster map using
regularized spline with tension (RST) algorithm.
vector, voxel, surface, interpolation, RST, 3D, nodata filling
v.vol.rst
v.vol.rst help
v.vol.rst [
c]
input=
name
[
cross_input=
name] [
wcolumn=
name]
[
tension=
float] [
smooth=
float]
[
smooth_column=
name] [
where=
sql_query]
[
deviations=
name] [
cvdev=
name]
[
maskmap=
name] [
segmax=
integer]
[
npmin=
integer] [
npmax=
integer]
[
dmin=
float] [
wscale=
float]
[
zscale=
float] [
cross_output=
name]
[
elevation=
name] [
gradient=
name]
[
aspect_horizontal=
name] [
aspect_vertical=
name]
[
ncurvature=
name] [
gcurvature=
name]
[
mcurvature=
name] [
overwrite] [
help]
[
verbose] [
quiet] [
ui]
 c

Perform a crossvalidation procedure without volume interpolation
 overwrite

Allow output files to overwrite existing files
 help

Print usage summary
 verbose

Verbose module output
 quiet

Quiet module output
 ui

Force launching GUI dialog
 input=name [required]

Name of input 3D vector points map
 cross_input=name

Name of input surface raster map for crosssection
 wcolumn=name

Name of column containing wvalues attribute to interpolate
 tension=float

Tension parameter
Default: 40.
 smooth=float

Smoothing parameter
Default: 0.1
 smooth_column=name

Name of column with smoothing parameters
 where=sql_query

WHERE conditions of SQL statement without ’where’ keyword
Example: income < 1000 and population >= 10000
 deviations=name

Name for output deviations vector point map
 cvdev=name

Name for output crossvalidation errors vector point map
 maskmap=name

Name of input raster map used as mask
 segmax=integer

Maximum number of points in a segment
Default: 50
 npmin=integer

Minimum number of points for approximation in a segment (>segmax)
Default: 200
 npmax=integer

Maximum number of points for approximation in a segment (>npmin)
Default: 700
 dmin=float

Minimum distance between points (to remove almost identical points)
 wscale=float

Conversion factor for wvalues used for interpolation
Default: 1.0
 zscale=float

Conversion factor for zvalues
Default: 1.0
 cross_output=name

Name for output crosssection raster map
 elevation=name

Name for output elevation 3D raster map
 gradient=name

Name for output gradient magnitude 3D raster map
 aspect_horizontal=name

Name for output gradient horizontal angle 3D raster map
 aspect_vertical=name

Name for output gradient vertical angle 3D raster map
 ncurvature=name

Name for output change of gradient 3D raster map
 gcurvature=name

Name for output Gaussian curvature 3D raster map
 mcurvature=name

Name for output mean curvature 3D raster map
v.vol.rst interpolates values to a 3dimensional raster map from
3dimensional point data (e.g. temperature, rainfall data from climatic
stations, concentrations from drill holes etc.) given in a 3D vector point
file named
input. The size of the output 3D raster map
elevation
is given by the current 3D region. Sometimes, the user may want to get a 2D
map showing a modelled phenomenon at a crossection surface. In that case,
cross_input and
cross_output options must be specified, with the
output 2D raster map
cross_output containing the crossection of the
interpolated volume with a surface defined by
cross_input 2D raster
map. As an option, simultaneously with interpolation, geometric parameters of
the interpolated phenomenon can be computed (magnitude of gradient, direction
of gradient defined by horizontal and vertical angles), change of gradient,
GaussKronecker curvature, or mean curvature). These geometric parameteres are
saved as 3D raster maps
gradient, aspect_horizontal, aspect_vertical,
ncurvature, gcurvature, mcurvature, respectively. Maps
aspect_horizontal and
aspect_vertical are in degrees.
At first, data points are checked for identical positions and points that are
closer to each other than given
dmin are removed. Parameters
wscale and
zscale allow the user to rescale the wvalues and
zcoordinates of the point data (useful e.g. for transformation of elevations
given in feet to meters, so that the proper values of gradient and curvatures
can be computed). Rescaling of zcoordinates (
zscale) is also needed
when the distances in vertical direction are much smaller than the horizontal
distances; if that is the case, the value of
zscale should be selected
so that the vertical and horizontal distances have about the same magnitude.
Regularized spline with tension method is used in the interpolation. The
tension parameter controls the distance over which each given point
influences the resulting volume (with very high tension, each point influences
only its close neighborhood and the volume goes rapidly to trend between the
points). Higher values of tension parameter reduce the overshoots that can
appear in volumes with rapid change of gradient. For noisy data, it is
possible to define a global smoothing parameter,
smooth. With the
smoothing parameter set to zero (
smooth=0) the resulting volume passes
exactly through the data points. When smoothing is used, it is possible to
output a vector map
deviations containing deviations of the resulting
volume from the given data.
The user can define a 2D raster map named
maskmap, which will be used as
a mask. The interpolation is skipped for 3dimensional cells whose
2dimensional projection has a zero value in the mask. Zero values will be
assigned to these cells in all output 3D raster maps.
If the number of given points is greater than 700, segmented processing is used.
The region is split into 3dimensional "box" segments, each having
less than
segmax points and interpolation is performed on each segment
of the region. To ensure the smooth connection of segments, the interpolation
function for each segment is computed using the points in the given segment
and the points in its neighborhood. The minimum number of points taken for
interpolation is controlled by
npmin , the value of which must be
larger than
segmax and less than 700. This limit of 700 was selected to
ensure the numerical stability and efficiency of the algorithm.
Using the
where parameter, the interpolation can be limited to use only a
subset of the input vectors.
# preparation as in above example
v.vol.rst elevrand_3d wcol=soilrange elevation=soilrange zscale=100 where="soilrange > 3"
Sometimes it can be difficult to figure out the proper values of interpolation
parameters. In this case, the user can use a crossvalidation procedure using
c flag (a.k.a. "jackknife" method) to find optimal
parameters for given data. In this method, every point in the input point file
is temporarily excluded from the computation and interpolation error for this
point location is computed. During this procedure no output grid files can be
simultanuously computed. The procedure for larger datasets may take a very
long time, so it might be worth to use just a sample data representing the
whole dataset.
Example (based on Slovakia3d dataset):
v.info c precip3d
g.region n=5530000 s=5275000 w=4186000 e=4631000 res=500 p
v.vol.rst c input=precip3d wcolumn=precip zscale=50 segmax=700 cvdev=cvdevmap tension=10
v.db.select cvdevmap
v.univar cvdevmap col=flt1 type=point
Based on these results, the parameters will have to be optimized. It is
recommended to plot the CV error as curve while modifying the parameters.
The best approach is to start with
tension,
smooth and
zscale with rough steps, or to set
zscale to a constant
somewhere between 3060. This helps to find minimal RMSE values while then
finer steps can be used in all parameters. The reasonable range is
tension=10...100,
smooth=0.1...1.0,
zscale=10...100.
In
v.vol.rst the tension parameter is much more sensitive to changes than
in
v.surf.rst, therefore the user should always check the result by
visual inspection. Minimizing CV does not always provide the best result,
especially when the density of data are insufficient. Then the optimal result
found by CV is an oversmoothed surface.
The vector points map must be a 3D vector map (x, y, z as geometry). The module
v.in.db can be used to generate a 3D vector map from a table containing x,y,z
columns. Also, the input data should be in a projected coordinate system, such
as Universal Transverse Mercator. The module does not appear to have support
for geographic (Lat/Long) coordinates as of May 2009.
v.vol.rst uses regularized spline with tension for interpolation from
point data (as described in Mitasova and Mitas, 1993). The implementation has
an improved segmentation procedure based on Octtrees which enhances the
efficiency for large data sets.
Geometric parameters  magnitude of gradient (
gradient), horizontal (
aspect_horizontal) and vertical (
aspect_vertical)aspects, change
of gradient (
ncurvature), GaussKronecker (
gcurvature) and mean
curvatures (
mcurvature) are computed directly from the interpolation
function so that the important relationships between these parameters are
preserved. More information on these parameters can be found in Mitasova et
al., 1995 or Thorpe, 1979.
The program gives warning when significant overshoots appear and higher tension
should be used. However, with tension too high the resulting volume will have
local maximum in each given point and everywhere else the volume goes rapidly
to trend. With a smoothing parameter greater than zero, the volume will not
pass through the data points and the higher the parameter the closer the
volume will be to the trend. For theory on smoothing with splines see Talmi
and Gilat, 1977 or Wahba, 1990.
If a visible connection of segments appears, the program should be rerun with
higher
npmin to get more points from the neighborhood of given segment.
If the number of points in a vector map is less than 400,
segmax should
be set to 400 so that segmentation is not performed when it is not necessary.
The program gives a warning when the user wants to interpolate outside the
"box" given by minimum and maximum coordinates in the input vector
map. To remedy this, zoom into the area encompassing the input vector data
points.
For large data sets (thousands of data points), it is suggested to zoom into a
smaller representative area and test whether the parameters chosen (e.g.
defaults) are appropriate.
The user must run
g.region before the program to set the 3D region for
interpolation.
Spearfish example (we first simulate 3D soil range data):
g.region dp
# define volume
g.region res=100 tbres=100 res3=100 b=0 t=1500 ap3
### First part: generate synthetic 3D data (true 3D soil data preferred)
# generate random positions from elevation map (2D)
r.random elevation.10m vector_output=elevrand n=200
# generate synthetic values
v.db.addcolumn elevrand col="x double precision, y double precision"
v.to.db elevrand option=coor col=x,y
v.db.select elevrand
# create new 3D map
v.in.db elevrand out=elevrand_3d x=x y=y z=value key=cat
v.info c elevrand_3d
v.info t elevrand_3d
# remove the now superfluous ’x’, ’y’ and ’value’ (z) columns
v.db.dropcolumn elevrand_3d col=x
v.db.dropcolumn elevrand_3d col=y
v.db.dropcolumn elevrand_3d col=value
# add attribute to have data available for 3D interpolation
# (Soil range types taken from the USDA Soil Survey)
d.mon wx0
d.rast soils.range
d.vect elevrand_3d
v.db.addcolumn elevrand_3d col="soilrange integer"
v.what.rast elevrand_3d col=soilrange rast=soils.range
# fix 0 (no data in raster map) to NULL:
v.db.update elevrand_3d col=soilrange value=NULL where="soilrange=0"
v.db.select elevrand_3d
# optionally: check 3D points in Paraview
v.out.vtk input=elevrand_3d output=elevrand_3d.vtk type=point dp=2
paraview data=elevrand_3d.vtk
### Second part: 3D interpolation from 3D point data
# interpolate volume to "soilrange" voxel map
v.vol.rst input=elevrand_3d wcol=soilrange elevation=soilrange zscale=100
# visualize I: in GRASS GIS wxGUI
g.gui
# load: 2D raster map: elevation.10m
# 3D raster map: soilrange
# visualize II: export to Paraview
r.mapcalc "bottom = 0.0"
r3.out.vtk s input=soilrange top=elevation.10m bottom=bottom dp=2 output=volume.vtk
paraview data=volume.vtk
deviations file is written as 2D and deviations are not written as
attributes.
Hofierka J., Parajka J., Mitasova H., Mitas L., 2002, Multivariate Interpolation
of Precipitation Using Regularized Spline with Tension. Transactions in GIS 6,
pp. 135150.
Mitas, L., Mitasova, H., 1999, Spatial Interpolation. In: P.Longley, M.F.
Goodchild, D.J. Maguire, D.W.Rhind (Eds.), Geographical Information Systems:
Principles, Techniques, Management and Applications, Wiley, pp.481492
Mitas L., Brown W. M., Mitasova H., 1997, Role of dynamic cartography in
simulations of landscape processes based on multivariate fields. Computers
and Geosciences, Vol. 23, No. 4, pp. 437446 (includes CDROM and WWW:
www.elsevier.nl/locate/cgvis)
Mitasova H., Mitas L., Brown W.M., D.P. Gerdes, I. Kosinovsky, Baker, T.1995,
Modeling spatially and temporally distributed phenomena: New methods and tools
for GRASS GIS. International Journal of GIS, 9 (4), special issue on
Integrating GIS and Environmental modeling, 433446.
Mitasova, H., Mitas, L., Brown, B., Kosinovsky, I., Baker, T., Gerdes, D.
(1994): Multidimensional interpolation and visualization in GRASS GIS
Mitasova H. and Mitas L. 1993: Interpolation by Regularized Spline with Tension:
I. Theory and Implementation,
Mathematical Geology 25, 641655.
Mitasova H. and Hofierka J. 1993: Interpolation by Regularized Spline with
Tension: II. Application to Terrain Modeling and Surface Geometry Analysis,
Mathematical Geology 25, 657667.
Mitasova, H., 1992 : New capabilities for interpolation and topographic analysis
in GRASS, GRASSclippings 6, No.2 (summer), p.13.
Wahba, G., 1990 : Spline Models for Observational Data, CNMSNSF Regional
Conference series in applied mathematics, 59, SIAM, Philadelphia,
Pennsylvania.
Mitas, L., Mitasova H., 1988 : General variational approach to the interpolation
problem, Computers and Mathematics with Applications 16, p. 983
Talmi, A. and Gilat, G., 1977 : Method for Smooth Approximation of Data, Journal
of Computational Physics, 23, p.93123.
Thorpe, J. A. (1979): Elementary Topics in Differential Geometry.
SpringerVerlag, New York, pp. 694.
g.region, v.in.ascii, r3.mask, v.in.db,
v.surf.rst, v.univar
Original version of program (in FORTRAN) and GRASS enhancements:
Lubos Mitas, NCSA, University of Illinois at UrbanaChampaign, Illinois, USA,
since 2000 at Department of Physics, North Carolina State University, Raleigh,
USA lubos_mitas@ncsu.edu
Helena Mitasova, Department of Marine, Earth and Atmospheric Sciences, North
Carolina State University, Raleigh, USA, hmitaso@unity.ncsu.edu
Modified program (translated to C, adapted for GRASS, new segmentation
procedure):
Irina Kosinovsky, US Army CERL, Champaign, Illinois, USA
Dave Gerdes, US Army CERL, Champaign, Illinois, USA
Modifications for g3d library, geometric parameters, crossvalidation,
deviations:
Jaro Hofierka, Department of Geography and Regional Development, University of
Presov, Presov, Slovakia, hofierka@fhpv.unipo.sk, http://www.geomodel.sk
Last changed: $Date: 20161114 00:05:32 +0100 (Mon, 14 Nov 2016) $
Available at: v.vol.rst source code (history)
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